In the latest release, OpenOffice's efforts to overhaul the interface have been restricted largely to the sidebar, an feature that has to be specifically enabled in LibreOffice from Tools -> Options -> LibreOffice -> Advance, and is labeled as "experimental."
The sidebar is a collection of features, primarily for manual formatting. Since this use comes at the expense of encouraging the use of styles, as the logic of the code intends, it is easy to dismiss. However, at its best, the sidebar is an immense simplification of some of the tabs for formatting characters and paragraphs, such as the Border tab in all applications, and the Format tab for spreadsheet cells. With luck, its re-conceptualization of controls will eventually find its way to the menus and style dialogue windows.
LibreOffice has been even more adventuresome. For example, the task pane in Impress, while similar to the sidebar, summarizes most of the steps in slide design in the names of its tabs.
But it is the Writer editing window where most of LibreOffice's interface improvements have taken place. A word and character count has been added to the status bar at the bottom of the window, and the cramped sub-menus for managing and editing templates have been replaced with a stream-lined interface in which buttons replace drop-down menus.
Even more obvious, the main text frame has been reduced in LibreOffice to cross-hairs at the four corners. In the same way, headers and footers are invisible until you click where they should be, when four small right angles indicate their borders.
A less successful effort is a tab in LibreOffice's editing window for managing headers and footers. Aside from the fact that the tab encourages manual formatting, it has the annoying habit of hiding part of the first line of a new page as it is typed.
These efforts are far from complete, although LibreOffice has also rearranged options in a number of dialogue windows. At times, they make LibreOffice a disconcerting mixture of vintage interfaces and modern minimalism that can be disconcerting to move between. However, at least LibreOffice is trying to address the long-delayed problem of the interfaces -- something OpenOffice has not had much time to consider.
An average user, whose documents are rarely longer than two or three pages, would often have to check the title bar to be sure whether they were using LibreOffice or OpenOffice. However, depending on their needs, advanced users will probably find LibreOffice currently has a small, but definite advantage.
This advantage is hardly to be unexpected. For one thing, LibreOffice had many months to advance while OpenOffice was concerned with setting up governance and doing a code audit. These tasks might be useful and necessary, but they do not make for improvements in the code that ordinary users are likely to notice.
For another, the LibreOffice fork was begun largely by members of Go-oo, an unofficial fork of OpenOffice.org that wanted to accelerate change. While Apache OpenOffice was forming, LibreOffice attracted talent around the world who wanted to code and were excited by the idea that everything was suddenly up for reconsideration.
Nobody has any done a census, but my impression is that when the OpenOffice.org community divided, the more adventurous contributors chose to focus on LibreOffice, although a few, such as the semi-independent documentation team, deliberately work for both projects.
However, the most important advantage for LibreOffice is what might be called the license-drain. That is, while the Apache License is compatible with LibreOffice's Lesser GNU General Public License, the Less GNU General Public License is incompatible with the Apache License. In other words, while LibreOffice can borrow code freely from OpenOffice, OpenOffice cannot borrow at all from LibreOffice. Strictly speaking, it must do clean-room implementations of features it wants to borrow from LibreOffice.
This situation may change, especially since Apache OpenOffice enjoys enormous name recognition compared to LibreOffice. Yet LibreOffice has quickly earned widespread support and has an active community that has done more in three years than OpenOffice.org managed in twelve.
For now, whether you use Apache OpenOffice or LibreOffice is likely to make very little difference unless you need a particular feature. However, I suspect that, unless something unexpected happens, LibreOffice's slight advantage is only going to widen. Whichever you decide on, you may want to schedule a re-evaluation in a few years' time.